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# L10 superconductivity

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• ### L10 superconductivity

1. 1. Lecture 10 Friday, 04 Feb 2011 Superconductivity 10-01. Who is going to win the big game on Sunday? 1. Green Bay Packers 2. Pittsburgh Steelers 3. What game on Sunday? 4. I couldn’t care less, because I only watch the commercials!
2. 2. Commitment to Excellence
3. 3. RC-Circuit <ul><li>What happens when the switch S is closed? </li></ul><ul><li>What happens to the voltage across R? </li></ul><ul><li>What happens to the voltage across C? </li></ul>
4. 4. The instant that S is closed, charge (e + ) begins to flow from the upper plate of C through R to cathode of the battery AND from the anode of the battery to lower plate of C. The net charge on C slowly builds until Q = CE, at which point the current is zero. The current through R is initially E/R, but as the net charge on C builds, the potential drop across R, and hence the current through R, slowly declines, ultimately to zero.
5. 5. As the net charge on C builds to its final value, CE, the potential drop across R declines from E to zero and the potential drop across C increases from zero to E.
6. 6. RC-Circuit <ul><li>Now let’s go through the math . . . </li></ul>Starting at point A and moving ccw: + E – q / C – R i = 0 R ( dq / dt ) + q / C = E dq / ( C E – q) = dt / (RC) Q = C E ( 1 – e - t / RC )  (time constant) = R C A
7. 7. RC-Circuit for auto turn signal or cardiac pacemaker
8. 8. ConcepTest 09-08 (dis) Capacitors <ul><li>After switch S is closed, what will the bulb do? </li></ul>(1) nothing (2) glow steadily at constant brightness (3) glow brightly, but slowly fade out. (4) slowly grow to full brightness.
9. 9. ConcepTest 09-08 (Post) Capacitors <ul><li>After switch S is closed, what will the bulb do? </li></ul>(1) nothing (2) glow steadily at constant brightness (3) glow brightly, but slowly fade out. (4) slowly grow to full brightness. The initial surge of charge from right capacitor plate to the battery and from the battery to the left capacitor plate will cause the bulb to glow. As the net charge on the capacitor builds to its final value, the bulb will slowly fade out.
10. 10. <ul><li>A microwave oven draws 0.8 A when connected to a 120 V outlet. What is the cost of running the oven to heat a cup of coffee for 1.5 minutes. PEPCO, the local electrical power (really “energy”) company, charges 3 cents per kWh. </li></ul>Cost of Energy Sample Problem How much energy is used? P = I V = (0.8 A)(120 V) = 96 W Energy = (Power)(time) = (96 J/s)(1.5 m)(60 s/m) = 8640 J Energy Used = 8.64 kJ Rate = 3¢/(kW-hr) = 3¢/[(10 3 J/s)(3600s)] = 8.33 x 10 -7 ¢/J Cost = (Energy Used)(Cost) = (8640 J)(8.33 x 10 -7 ¢/J) Cost = 7.2 x 10 -3 ¢ = 7.2 m¢
11. 11. How much charge is there in a battery?
12. 12. “ Mission Impossible” You are given a brand new flashlight with two new D-cell (1.5 V) batteries and an 1 W bulb. Your task, Mr. Phelps, should you decide to accept it, is to determine how much energy is stored in the two D-cell batteries. (This tape will self destruct in 10 sec. and the Secretary will disavow any knowledge of its existence.) Assuming you accepted the task, how would you determine the answer?
13. 13. Turn the flashlight on and see how long the bulb stays lit. Suppose the bulb remained lit for 18.3 hours. How much energy was dissipated in the filament of the bulb? It is a 1 W bulb, therefore it converts 1 J of stored chemical energy in the batteries into light and heat every second: Energy = (power)(time) = (1 J/s)(18.3 hr)(3600 s/hr) Energy = 6.59 x 10 4 J = 65.9 kJ. How many electrons will have moved through the filament by the time the light goes out?
14. 14. How many electrons will have moved through the filament by the time the light goes out? What is the current that flowed through the filament during those 18.3 hours? P = I V so I = P/V = (1 W)/(1.5 V + 1.5 V) = 0.33 A That is, 0.33 C/s. So how many C flowed through the filament? (0.33 C/s)(18.3 hr)(3600 s/hr) = 2.20 x 10 4 C And how many electrons is that? # e - = Q / e - = (2.20 x 10 4 C)/(1.6 x 10 -19 C/e - ) #e = 1.37 x 10 23 electrons.
15. 15. Here comes another one of those &quot; When I was, where you are now...&quot; stories. When I was, where you are now, give or take a few years, I found myself always sitting next to Bob Simon — Why? Bob and I became good friends and a life long QSO got started...
16. 16. ... and on the inside of the front cover, Heathkit provided a very handy table so that you could identify each of the circuit elements with their schematic representation on the schematic diagram
17. 17. Schematic Diagram of a 20-m SSB Transceiver
18. 18. Integrated circuits (IC's) combine &quot;active&quot; electronic devices (transistors and diodes) with passive elements (capacitors and resistors) on a single semi-conductor crystal. The actual size of the &quot;chip&quot; on the left is a 6.4 mm square; there are 44 connector leads. This device digitizes voice and data signals so that they can share a single transmission line. The figure on the right is an SEM microphotograph showing two conductor leads precision bonded to the edge of a &quot;chip&quot; (magnification: x163).
19. 19. The &quot;chip&quot; between the tweezers holds 150,000 transistors. Beneath the chip is a 4 inch wide Si wafer awaiting &quot;dicing&quot;, on which a group of chips have been fabricated simultaneously. In the background is a detail of the &quot;stare plot&quot; , the layout of the chips circuits and the modern equivalent of the &quot;old fashioned&quot; schematic diagram.
20. 20. Superconductivity New Topic
21. 21. Agenda for Today <ul><li>History of superconductivity </li></ul><ul><li>Properties of superconductors (Meissner Effect; magnetic levitation) </li></ul><ul><li>Possible applications of superconductivity </li></ul><ul><li>Superconducting materials (There are a lot of ‘em!) </li></ul><ul><li>BCS Theory </li></ul><ul><li>Having a Nobel Prize does not guarantee that you will not do something very, VERY STUPID! </li></ul><ul><li>Many false claims: CdS, CuCl, TTF-TCNQ  It’s OK to make an error </li></ul><ul><li>The Revolution … and the Woodstock of the APS </li></ul><ul><li>Skelton’s greatest scientific blunder </li></ul><ul><li>A little trickery: YbBa 2 Cu 3 O 7 = YBa 2 Cu 3 O 7 </li></ul><ul><li>Efforts to discover a simpler superconductor  a failure </li></ul><ul><li>T c (P) can be important  A World Record!! (for 3 months anyway) </li></ul><ul><li>Discovery of microscopic inhomogeneities </li></ul>
22. 22. PLQ for Lecture 10 <ul><li>PLQ-10, which opened at 6 AM today, Friday, 04 Feb 2011, and closes at the usual time, 6 AM on Monday, contains ten (10) questions. </li></ul><ul><li>Because the answers to all the questions in PLQ-10 are contained in the PPT slides presented in Lecture 10, you have only one try for #1  #8 … but many of the same questions are covered in the PRS questions in L10. </li></ul><ul><li>------------------------------------------------------------------------- </li></ul><ul><li>Superconductivity is covered in Section 25-9 on p. 650 of the text. </li></ul>
23. 23. This is a conductor  and this is a SUPERCONDUCTOR  This is a semiconductor  Let’s talk a little about superconductivity. There are no CPS problems on superconductivity; there are a few PRS questions included to “hold your attention”; the ten PLQs for this lecture are all answered in the following PPT slides and there probably will be a question about superconductivity on MT1.
24. 24. Superconductivity: In 1911, H. Kamerlingh Onnes, working at Leiden University in The Netherlands, thought that his apparatus had broken. After repeated experiments he wrote the following words in his research journal:
25. 25. The most spectacular effect of superconductivity is the complete absence of any resistance to the passage of an electrical current. Another property of all superconductors is the Meissner Effect, the complete expulsion of a magnetic field from the superconducting material. This property leads to magnetic levitation . .
26. 26. Permanent magnet, e.g., Fe 3 O 4 (magnetite) YBa 2 Cu 3 O 10-  , one of the newest high T c superconductors See Fig. 25-26 in the text for a photo of a magnetically levitated train.
27. 27. The practical applications of superconductivity are significant and numerous. Here are a few: 1. Electric transmission lines . 2. Electric motors and generators
28. 28. The practical applications of superconductivity are significant and numerous. Here are a few more: 4. Electric circuits, e.g. computers and high field magnets (X17C) . . . 3. Magnetic levitation
29. 29. Most metals are superconducting. See the following tabulations.
30. 30. There are 32 superconducting elements listed here, from Al to W. The highest value of T c is 9.25 + 0.02 K in Nb.
31. 31. This is the first page of a tabulation of superconducting materials listing various Ag compounds:
32. 32. This is the 50 th page of the same tabulation. I estimate ~25 compounds/page which gives ~1250 known superconductors as of 1978. Source: Properties of Superconducting Materials. (NBS, 1978)
33. 33. There are 3 ways to destroy superconductivity, i.e ., drive a superconductor normal: T c , J c , and H c .
34. 34. The theory of what is now called “classical superconductivity” was solved in 1957 by three physicists at the University of Illinois, John Bardeen, Leon Cooper, and Robert Schreiffer. Today this theory is known as “BCS-Theory.” [N.B.: 1957 – 1911 = 46 years] BCS theory involves two revolutionary concepts: 1. Cooper pairs: Electrons that are bonded together 2. Electron – phonon interactions: The Cooper pairs that interact with the lattice vibrations in an ultra-harmonious manner.
35. 35. John Bardeen (May 23, 1908 – January 30, 1991) was an American physicist and electrical engineer. He is the only person to have won two Nobel Prizes in Physics: in 1956 for inventing the transistor, along with William Shockley and Walter Brattain, and in 1972 for a fundamental theory of conventional superconductivity known as the BCS theory, together with Leon Neil Cooper and John Robert Schrieffer. He was the first person to win two Nobel Prizes in the same field. The transistor revolutionized the electronics industry, allowing the Information Age to occur, and made possible the development of almost every modern electronic device, from telephones to computers to missiles. His developments in superconductivity, which won him his second Nobel, are used in medical advances such as CAT scans and MRI. Dr. John Bardeen (1908-1991)
36. 36. First page of the publication in The Physical Review (Phys. Rev.) for which B, C, and S were awarded the Nobel Prize in 1972. Winning a Nobel Prize does not prevent you from doing something very, VERY STUPID!
37. 38. There is absolutely nothing in BCS-Theory that limits the value of T c . So, according to BCS-Theory, it is possible to have a room temperature superconductor. However, from 1911 until 1973, the maximum value of T c had increased only from 4.2 K in Hg to 23.2 K in Nb 3 Ge. And there were many false claims . . .
38. 39. By 1973, the highest known T c had increased from 4.2 K to 23.2 K in Nb 3 Ge. 23.2K 1973 Nb 3 Ge 4.2K 1911 Hg
39. 40. L10-02: PRS Test 1 (1) Bendorez and Muller in 1987 in La 2 CuO 4 (2) Kirchhoff in 1923 in tin oxide (SnO) (3) H. Kamerling Onnes in 1911 in mercury (Hg) (4) John Bardeen in 1927 in YBa 2 Cu 3 O 10-  (4) Leon Cooper in 1957 in Nb 3 Ge (6) None of the above Who first discovered superconductivity, in what year, and in what material?
40. 41. L10-03: PRS Test 2 (1) Magnetic levitation (2) Electrical circuits (3) Electric motors and generators (4) Electric heating elements, such as space heaters, electric stoves, and toasters (5) Electric transmission lines (6) All of the above are possible applications of superconductivity. Which, if any, of the items on the right is/are NOT possible applications of superconductivity?
41. 42. L10-04: PRS Test 3 (1) Electron density of states (2) Cryogenic cooling (3) Meissner effect (4) Magnetic levitation (5) Electron-coupling (Cooper pairs) (6) Electron degeneracy pressure What new, revolutionary concept was introduced in BCS-Theory?
42. 43. L10-05: PRS Test 4 (1) pressure induced disproportionation (2) the Meissner effect (3) Cooper pairing (4) magnetic levitation (5) cryogenic cooling What is demonstrated in the figure at the right?
43. 44. False Reports New Topic
44. 46. Electrical conductivity of tetrathiofulvalinium tetracyanoquinodimethan (TTF-TCNQ) Marshall J. Cohen*, L. B. Coleman*,§, A. F. Garito, and A. J. Heeger Department of Physics and Laboratory for Research on the Structure of Matter, University of Pennsylvania, Philadelphia, Pennsylvania 19174 (Received 20 February 1974) The temperature dependence of the dc electrical conductivity of tetrathiofulvalinium tetracyanoquinodimethan (TTF)(TCNQ) measured along the crystallographic a, b, and c* axes and the corresponding anisotropies sigma b|| / sigma aperp and sigma b|| / sigma c*perp are reported. Standard four-probe measurements are supplemented by applying the technique of Montgomery to the question of inhomogeneous currents in this anisotropic conductor. We have observed that the intrinsic anisotropy contains two maxima which provide a direct internal method for unambiguously testing the validity of four-probe measurements of the conductivity along the principal conducting b axis. The transverse transport properties are diffusive and yield an electrical anisotropy greater than 500 at room temperature which increases to greater than 104 near 58 K. The extreme sensitivity of this one-dimensional metal to crystalline imperfections is experimentally demonstrated through temperature cycling studies. The dc results confirm (TTF)(TCNQ) is a one-dimensional metal exhibiting a strongly temperature-dependent b-axis conductivity that reaches maximum values exceeding 105 ( Omega cm)-. These data are taken as confirming evidence that above 58 K the metallic state exhibits strong electron correlations associated with a many-body collective state in which the conductivity can greatly exceed the limitations of single-particle scattering. ©1974 The American Physical Society
45. 47. Tetrathiofulvalinum tetracyanoquinodimethane (TTF-TCNQ) was reported superconducting in the early 1970’s by Alan Heeger et al. from U. Penn. “ No evidence of a multiplicative enlargement of the unit cell in a direction parallel to the conducting chains has been observed.” Heeger won the 2000 Nobel Prize in Chemistry for his work on these materials. Upshot: It’s okay to make a mistake.
46. 48. In 1978, I got a telephone call from the CIA. The Soviets were reporting super- conductivity at ~90 K in CuCl (and the Cold War was still “hot”!) Is it real?
47. 49. Micro-photographs taken through a diamond-anvil pressure cell of freshly prepared CuCl as a function of time: a. immediately after pressurization b. about 10 min. later c. about 30 min. later d. the next day a. c. b. d.
48. 50. Very tenuous evidence of pressure induced disproportionation, i.e. , 2 CuCl  CuCl 2 + Cu based on ESR data.
49. 51. “ ... no evidence is found to support the existence of a superconducting transition in the interval between 300 and ~10 K and at pressures up to about 10 GPa.”
50. 52. Synchrotron x-ray data taken at SSRL showing definitive evidence of pressure induced disproportion-ation in the isomorphic compound CuBr:
51. 54. Superconductivity Revolution New Topic
52. 55. In Oct 1986, Bednorz and Muller, working at the IBM Research Lab. in Zurich, Switzerland, reported the possibility of high T c superconductivity in a compound of Ba-La-Cu-O. :
53. 58. L10-06: PRS Test 5 (1) CdS (2) TTF-TCNQ (3) CuCl (4) all of the above Which material on the right was reported to be a high T c superconductor, but was not?
54. 59. PRS Test 10-07: 1) The CuCl samples used in the original experiments were contaminated. 2) The electrical circuits used in the original experiment were flawed. 3) Pressure induced disproportionation: 2 CuCl  CuCl 2 + Cu 4) Mixing of the CuCl sample in the test chamber with chemicals in the high pressure fluid 5) Inadvertent deposition of conductive material on the surface of the CuCl test sample 6) The reason for the unusual electrical properties in CuCl are still not understood. What was the explanation for the unusual electrical properties of CuCl that were first thought to be superconductivity?
55. 60. In March 1987, ~ 95% of all American physicists working in the field of superconductivity were gathered in NYC for the annual APS Meeting, the Woodstock of the APS . Was Skelton there? “ N o o ooooo . . .” Skelton was back in his lab at NRL working “24/7” on an experiment that was going to be the basis for a trip to Stockholm . . . but which turned out to be . . . and the Nobel Prize! Skelton's Greatest Scientific Blunder!
56. 61. X-Ray Diffraction Patterns from La 2 CuO 4 vs. T
57. 62. Simultaneous R ( T ) and I ( T ) on La 2 CuO 4
58. 63. Independent theoretical prediction of the “Skelton Transition”
59. 64. How physics works: Physicists are divided into two groups: theorists and experimentalists. Theorists work on theories; experimentalists do experiments. When a member of either group comes up with something “new”, s/he writes a paper about it and submits that paper to a journal for publication. There are journals and then there are JOURNALS Nature Science ---------------------------------------------- Physical Review Letters Physical Review – Rapid ---------------------------------------------- Physical Review Review of Scientific Instruments American Journal of Physics Solid State Communications Acta Crystallographica . . . (journals that will publish anything)
60. 65. First publication of the “Skelton Transition”:
61. 66. Second publication of the “Skelton Transition”: Rapid Communication
62. 67. The sad story of how the truth slowly came out will be related in class.
63. 68. X-Ray Diffraction Patterns from La 2 CuO 4 vs. T
64. 69. Demise of the “Skelton Transition” and the Nobel Prize: The nitrogen    phase transition occurs at the same temperature as the electronic transition in La 2 CuO 4 !!! What an embarrassment!!!
65. 70. Most scientists are very honest . . . A little trickery: YbBa 2 Cu 3 O 7 = YBa 2 Cu 3 O 7
66. 71. In the paper that Chu, Wu, et al. submitted for publication to Phys. Rev. Lett., the 93 K superconductor was reported as YbBa 2 Cu 3 O 7 . The alleged “typographical” error of the composition was corrected to YBa 2 Cu 3 O 7 in the galley proofs.
67. 72. Search for a Single Cell Superconductor (LaCuO 3 ) New Topic
68. 73. In Oct 1986, Bednorz and Muller, working at the IBM Research Lab. in Zurich, Switzerland, reported the possibility of high T c superconductivity in a compound of Ba-La-Cu-O. :
69. 75. Try adding a little sodium! (Na)
70. 81. Number of new and unique perovskite compounds synthesized: 225 Number of new, superconducting materials discovered: 0
71. 83. T c (P) New Topic
72. 87. Rapid Communication
73. 89. Rapid Communication
74. 90. E. F. Skelton, A Record Breaking Superconductor, Missed, Physics Today 47 (2), 120 (1994).
75. 92. The Superconductivity Revolution <ul><li>1911 : H. K. Onnes discovered superconductivity in Hg; T c = 4.2 K </li></ul><ul><li>1976: Nb 3 Ge discovered; T c = 23.2 K </li></ul><ul><li>1987: La 1.8 Sr 0.2 (or Ba 0.2 )CuO 4 ; T c = 35 K </li></ul><ul><li>1988: YBa 2 Cu 3 O 10-  ; T c = 93 K ( N.B. >77 K) </li></ul><ul><li>~1990: Hg-Ba-Ca-Cu-O; ; T c ~ 164 K </li></ul>... and we’re halfway there!
76. 93. The Superconductivity Revolution <ul><li>(Sn 1.0 Pb 0.5 In 0.5 )Ba 4 Tm 5 Cu 7 O 20+ ~185 K    (Patent Pending; March 2008) </li></ul>... and we’re almost 2 / 3 of the way there! Although cuprate compounds in the normal superconducting state share many characteristics with each other, there is, as of 2008, no widely accepted theory to explain their properties. The search for a theoretical understanding of high-temperature superconductivity is widely regarded as one of the most important unsolved problems in physics , and it continues to be a topic of intense experimental and theoretical research, with over 100,000 published papers on the subject. [1]
77. 94. Next, I will tell you how, in the late 1980’s, my Section at NRL discovered unequivocal evidence of microscopic inhomogeneities in the important high T c superconductor, YBa 2 Cu 3 O 10-  . First a few PRS questions to see if you’ve been awake for the last few minutes . . . Surprise!
78. 95. PRS Test 10-07: 1) 4.2 K in Hg 2) 23.2 K in Nb 3 Ge 3) 47 K in CuCl 2 4) 93 K in YBa 2 Cu 3 O 7-d 5) 35 K in La 1.8 (Ba or Sr) 0.2 CuO 4 6) 164 K in HgBa 2 Ca 2 Cu 3 O x 7) ~185 K in (Sn 1.0 Pb 0.5 In 0.5 )Ba 4 Tm 5 Cu 7 O 20+ What is the current (2008) record for the highest T c and in what material is it found?
79. 96. PRS Test 10-08: 1) Leon Cooper 2) Bob Schreiffer 3) Kamerlingh Onnes 4) Alan Heeger 5) John Bardeen 6) J. G. Bednorz 7) K. A. Muller 8) All of the above are Nobel Prize winners. Of the physicists at the right who worked in the field of superconductivity, which one did NOT receive a Nobel Prize for his work?
80. 97. Microscopic Inhomogeneities New Topic
81. 98. Evidence of Microscopic Inhomogeneities in YBa 2 Cu 3 O 10-  E. F. Skelton, S. B. Qadri, M. S. Osofsky, and V. M. Browning Condensed Matter and Radiation Sciences Division U. S. Naval Research Laboratory Washington, DC Owing to the absence of information to the contrary, samples of YBa 2 Cu 3 O 10-  , even single crystals, often are assumed to be homogeneous . . . . . . but it ain’t necessarily so!
82. 99. To determine the quality of YBCO samples, a variety of physical properties are examined, such as: 1. low resistivity values 2. linear  (T) plot 3. high T c 4. sharp superconducting transition 5. T 2 dependence of cot(  H ) 6. negative Hall anomaly 7. vortex lattice “melting” transition or seemingly good, “routine” x-ray data . . . . . . do not necessarily insure a HIGH QUALITY SAMPLE. Data obtained from such crystals may not represent intrinsic properties of YBCO.
83. 101. Camp Upton, Long Island, NY (ca. 1917) Brookhaven National Lab (today) NSLS at BNL
84. 102. X17C – “The World’s Hottest X-Ray Flame Thrower”
85. 108. 1 division = 0.020 mm = 20  m E. F. Skelton, A. R. Drews, M. S. Osofsky, S. B. Qadri, J. Z. Hu, T. A. Vanderah, J. L. Peng, and R. L. Greene, Direct Observation of Microscopic Inhomogeneities with Energy-Dispersive Diffraction of Synchrotron-Produced X-rays, Science 263 , 1416 (1994).
86. 109. YBa 2 Cu 3 O 7- 
87. 110. Conclusion: High quality macroscopic physical, superconducting data do NOT necessarily imply a uniform, homogeneous superconducting sample.
88. 111. This concludes our review of superconductivity. Thanks for your attention. I hope you now have a better understanding of both superconductivity and how modern science works!